Optimal. Leaf size=22 \[ \frac {x^7}{7}-\frac {8 x^5}{5}+\frac {16 x^3}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ \frac {x^7}{7}-\frac {8 x^5}{5}+\frac {16 x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 270
Rubi steps
\begin {align*} \int x^2 \left (4-x^2\right )^2 \, dx &=\int \left (16 x^2-8 x^4+x^6\right ) \, dx\\ &=\frac {16 x^3}{3}-\frac {8 x^5}{5}+\frac {x^7}{7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ \frac {x^7}{7}-\frac {8 x^5}{5}+\frac {16 x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 16, normalized size = 0.73 \[ \frac {1}{7} x^{7} - \frac {8}{5} x^{5} + \frac {16}{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.31, size = 16, normalized size = 0.73 \[ \frac {1}{7} \, x^{7} - \frac {8}{5} \, x^{5} + \frac {16}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 17, normalized size = 0.77 \[ \frac {1}{7} x^{7}-\frac {8}{5} x^{5}+\frac {16}{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.46, size = 16, normalized size = 0.73 \[ \frac {1}{7} \, x^{7} - \frac {8}{5} \, x^{5} + \frac {16}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 17, normalized size = 0.77 \[ \frac {x^3\,\left (15\,x^4-168\,x^2+560\right )}{105} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 17, normalized size = 0.77 \[ \frac {x^{7}}{7} - \frac {8 x^{5}}{5} + \frac {16 x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________